Method for Manufacturing Multi-Finger Pinned Root for Turbine Blade Attached to Turbine Rotor and Turbine Blade

ABSTRACT

In manufacturing a multi-finger pinned root pin-coupling a turbine blade made of a high-strength material and a rotor disc, a reamer used to ream a pin insertion hole formed through a turbine blade attachment base is removed from the pin insertion hole while being rotated so as to cause a scratch formed by a chip on the inner surface of the pin insertion hole to be inclined with respect to the axial direction of the pin insertion hole. This brings the direction of the scratch on the inner surface of the pin insertion hole and the direction of tensile stress generated on the inner surface of the pin insertion hole adequately close to be parallel to each other. As a result, the fatigue strength reduction caused by the scratch can be inhibited.

TECHNICAL FIELD

The present invention relates a method for manufacturing a multi-fingerpinned root for turbine blade attached to a turbine rotor and a turbineblade.

CLAIM OF PRIORITY

The present application claims priority from Japanese Patent applicationserial No. 2012-79867, filed on Mar. 30, 2012, the content of which ishereby incorporated by reference into this application.

BACKGROUND ART

A steam turbine for power generation has a rotary shaft referred to as aturbine rotor which is coupled with turbine blades. The turbine bladesrotate the turbine rotor by receiving steam power and cause electricpower to be generated. When the turbine rotor rotates, a centrifugalforce is generated in each turbine blade, and the centrifugal force issupported where the turbine blade is coupled with the turbine rotor. Theturbine blade and the turbine rotor can be coupled using, for example, apin and finger root form, a straddle mount form, or a fir-tree form. Aturbine blade and a turbine rotor coupled in the pin and finger rootform each have a fork-shaped part referred to as a fork. The turbineblade and the turbine rotor are coupled using coupling pins inserted inholes formed through them with their forks meshed with each other. Whenthe turbine rotor rotates, the centrifugal force generated in theturbine blade is supported by the coupling pins allowing a high stressto be circumferentially generated over the inner surface of each pininsertion hole. This results in a high risk of fatigue damage to theinner surface of each pin insertion hole. To reduce such a risk offatigue damage, it is necessary to pay particular attention to themachining accuracy for and the surface finish of each pin insertionhole.

To form a pin insertion hole through a part of a turbine where a turbinerotor and a turbine blade are coupled, a hole is drilled through thepart in a state with the turbine rotor fork and the turbine blade forkmeshed with each other, then each drilled hole is reamed to achieve atarget fitting accuracy and surface finish. This method of forming a pininsertion hole in which first a hole is drilled and next the drilledhole is reamed is described, for example, in Japanese Unexamined PatentPublication No. Sho 60(1985)-222503 (PTL1).

CITATION LIST Patent Literature

[PTL 1] Japanese Unexamined Patent Publication No. Sho 60(1985)-222503

Non Patent Literature

[NPTL1] Walter D. Pilkey, “Peterson's Stress Concentration Factors,”(USA), 2nd Edition, Wiley-Interscience, Apr. 18, 1997

SUMMARY OF INVENTION Technical Problem

For thermal power generation plants, there are cases in which, with anintention of adopting larger turbine blades, a high-strength bladematerial is used. In such cases, with a high-strength material havinghigh notch sensitivity, it is necessary to pay particular attention tothe surface finish of pin insertion holes so as to minimize theirsurface ruggedness.

If, while the surface of a drilled hole is being finished by reaming,chips attach to edges of the reamer, they detrimentally affect, asbuilt-up edges, the finish of the surface being reamed. Therefore, whilereaming a hole, air or cutting oil is kept applied to the hole portionbeing reamed so as to cause chips generated by reaming to be removedfrom the hole.

There are, however, cases in which fine chips generated during reamingof a pin insertion hole are left attached to edges of the reamer withoutbeing removed from the pin insertion hole and such chips result inleaving fine scratches on the inner surface of the pin insertion holewhen the reamer is removed from the pin insertion hole. According to thestudy made by the present inventors, in cases where a part through whichpin insertion holes are formed is made of a high-strength material, evenfine scratches left on the inner surface of a pin insertion hole whenthe reamer is removed from the pin insertion hole can detrimentallyaffect the fatigue strength of the part.

In the existing methods, including the one disclosed in PTL 1 (JapaneseUnexamined Patent Publication No. Sho 60(1985)-222503), for forming apin insertion hole through a turbine blade, no consideration is given toscratches generated by fine chips on the inner surface of a pininsertion hole when the reamer is removed from the pin insertion hole.When an existing method for forming a pin insertion hole through aturbine blade is applied, as it is, to a turbine blade made of ahigh-strength material with high notch sensitivity, the detrimentaleffect of scratches formed on the inner surface of a pin insertion holecannot be prevented.

An object of the present invention is to provide a method formanufacturing a multi-finger pinned root and a turbine blade, the methodbeing applicable with high strength reliability even to a turbine bladewhich is made of a high-strength material and which is to be coupled toa rotor in a pin and finger root form.

Solution to Problem

To achieve the above object, the present invention provides a method formanufacturing a multi-finger pinned root for turbine blade attached to aturbine rotor, the multi-finger pinned root coupling the turbine bladeand a rotor disc of the turbine rotor. In the method, after a pininsertion hole is reamed, the reamer used is removed from the pininsertion hole while being rotated.

The present invention also provides a turbine blade in which a scratchformed on the inner surface of a pin insertion hole formed through aroot portion to be pin-coupled to a rotor disc is inclined with respectto the axial direction of the pin insertion hole.

Advantageous Effects of Invention

According to the present invention, the direction of a scratch formed onthe inner surface of a pin insertion hole and the direction of tensilestress generated on the inner surface of the pin insertion hole areclose to be parallel to each other, so that fatigue strength reductiondue to the scratch can be inhibited.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a construction drawing of a turbine blade attachment base;

FIG. 2 is a schematic drawing of a reaming machine;

FIG. 3 is a schematic drawing of a reamer;

FIGS. 4A and 4B schematically show the inner surface of a pin insertionhole formed using a related-art technique; FIG. 4A being an enlargedview of the inner surface and FIG. 4B being a sectional view taken alongline A-A in FIG. 4A;

FIGS. 5A and 5B schematically show the inner surface of a pin insertionhole formed according to an embodiment of the present invention; FIG. 5Abeing an enlarged view of the inner surface and FIG. 5B being asectional view taken along line A-A in FIG. 5A;

FIG. 6 is a graph showing a relationship between stress range andfatigue life of a high-strength material;

FIG. 7 is a graph showing a relationship between stress concentrationfactor Kt and scratch inclination θ;

FIG. 8 is a drawing showing relationships between scratch inclination θ,reamer movement in rotational direction, and reamer movement in removaldirection; and

FIGS. 9A and 9B show a microscope; FIG. 9A being a schematic view andFIG. 9B being a sectional view of portion marked A in FIG. 9A.

DESCRIPTION OF EMBODIMENTS

An embodiment of the present invention will be described below withreference to drawings.

FIG. 1 is a construction drawing of a turbine blade attachment base. Theturbine blade attachment base is comprised of turbine blades 2 and aturbine rotor 3 combined together. Each turbine blade 2 has a bladesection 4 which receives a steam flow and converts the energy of thesteam flow into a rotational energy for the turbine and a blade fork 5.The turbine rotor 3 has a turbine rotary shaft 10 and a rotor disc 6provided circumferentially over the turbine rotary shaft 10. The rotordisc 6 has a rotor fork 7 formed thereon.

The blade fork 5 of the turbine blade 2 and the rotor fork 7 of theturbine rotor 3 are arranged to mesh with each other. The blade fork 5and the rotor fork 7 have pin insertion holes 8 extending through themin the rotor axis direction. Coupling pins 9 are inserted into the pininsertion holes 8 thereby filling the pin insertion holes 8 and fixingthe turbine blade 2 to the turbine rotor 3.

When the turbine rotates causing a centrifugal force in a radialdirection (an upward direction as seen in FIG. 1) to work on the turbineblade 2, the coupling pins 9 support the centrifugal force therebyallowing the turbine blade 2 to be kept coupled to the turbine rotor 3.As the coupling pins 9 support the centrifugal force working on theturbine blade 2 when the turbine rotor 3 rotates, a circumferentialtensile stress is generated over the inner surface of each pin insertionhole 8 resulting in a high risk of fatigue damage to the inner surfaceof each pin insertion hole 8. Hence, to reduce the fatigue damage risk,particular attention should be paid to the machining accuracy for andthe surface finish of each pin insertion hole 8.

The turbine blade is made of a high-strength material, for example, a Tialloy which allows the turbine blade to have a greater length. Ahigh-strength steel (with a tensile strength of 1300 MPa or higher) mayalso be used as a high-strength turbine blade material. Since, asmentioned in the foregoing, a high-strength material has high notchsensitivity, the surface finish of a turbine blade made of ahigh-strength material requires particular attention to be paid thereto.

To form the pin insertion holes 8 through the turbine blade attachmentbase, holes are drilled through the turbine rotor 3 and the turbineblade 2 with their forks meshed with each other, then the drilled holesare reamed to achieve target fitting accuracy and surface roughness.

FIG. 2 schematically shows a reaming machine 20. The reaming machine 20is made up of a reamer 21 used to finish each pin insertion hole drilledthrough the turbine fork 5 and the rotor fork 7 included in the turbineblade attachment base, a chuck section 22 for fixing the reamer 21 in adriving section, an arm 27 which includes the driving section and drivesthe driving section in the rotary axis direction, a mount 28 on whichthe arm 27 is mounted, and an air blower 23 for blowing chips attachingto the reamer 21 during reaming to outside the pin insertion hole beingreamed.

When chips generated during reaming attach to edges of the reamer 21,they detrimentally affect, as built-up edges, the surface of the pininsertion hole being reamed. To prevent this from occurring, the airblower 23 keeps blowing air into the pin insertion hole being reamed soas to remove chips 11 from the pin insertion hole 8. Still, there arecases in which, for example, a fine chip 12 remains, without being blownoff, attached to an edge of the reamer 21 as shown in FIG. 3 to resultin generating a fine scratch on the inner surface of the pin insertionhole when the reamer 21 is pulled out after reaming is finished.

FIG. 4A shows an enlarged view of the inner surface of a reamed pininsertion hole 8 in a state after the reamer 21 used is removed withoutbeing rotated (in a related-art case) and FIG. 4B shows a sectional viewtaken along line A-A in FIG. 4A. As shown in FIGS. 4A and 4B, the innersurface of the pin insertion hole 8 has a fine scratch 13 generated,along the axial direction of the pin insertion hole, by a fine chip 12.When the turbine rotor 3 rotates, a large stress is generatedcircumferentially along the inner surface of the pin insertion hole 8causing the stress to concentrate on a bottom 14 of the scratch 13generated by the fine chip 12. Hence, there is a risk of a fatigue crackbeing generated and growing along the bottom 14 of the scratch 13.

The depth a of the scratch is up to about 10 μm. In the case of steamturbines used at nuclear power generation plants, turbine blades aremade of steel with a tensile strength lower than 900 MPa, and thefatigue strength of such turbine blades are not detrimentally affectedby scratches with a depth of up to about 10 μm. In the case of thermalpower generation plants, however, there are cases in which, with anintention of adopting larger turbine blades, a higher-strength bladematerial is used. In the present embodiment, turbine blades made of ahigh-strength material are used so as to allow the turbine blades to bemade larger. Since high-strength materials have high notch sensitivity,their fatigue strength can possibly be affected detrimentally even byscratches 13 with a depth of about 10 μm generated by fine chips 12.

FIG. 5A shows an enlarged view of the inner surface of a reamed pininsertion hole 8 in a state after the reamer 21 used is removed whilebeing rotated under prescribed conditions according to an embodiment ofthe present invention and FIG. 5B shows a sectional view taken alongline A-A in FIG. 5A. In this case, when the reamer is removed from thepin insertion hole 8, the fine chip 12 is spirally pulled out generatinga scratch 15 inclined by an angle of θ with respect to the axialdirection of the pin insertion hole. Having the scratch formed with aninclination with respect to the axial direction of the pin insertionhole as shown in FIG. 5A can decrease the degree of stressconcentration, i.e. stress concentration factor Kt (=the stress at thebottom of the scratch divided by the stress with no scratch present) ona bottom 16 of the scratch. This will be described in detail in thefollowing. As for the increase of stress caused by a scratch, simplifiedcalculation is possible, for example, according to NPTL 1 (Walter D.Pilkey, “Peterson's Stress Concentration Factors,” (USA), 2nd Edition,Wiley-Interscience, Apr. 18, 1997).

First, with reference to FIGS. 4A and 4B, a related-art case in which,when the reamer used to ream a pin insertion hole is removed withoutbeing rotated, a scratch running along the axial direction of the pininsertion hole is formed on the inner surface of the pin insertion holewill be described. The sectional shape in the direction of stress of ascratch 13 generated by a chip can be approximated to a semi-ellipsewith depth a and width h. According to the above NPTL 1, the stressconcentration factor Kt in this case is represented by expression (1).

$\begin{matrix}{{Kt} = {1 + \frac{4\; a}{h}}} & (1)\end{matrix}$

With the ratio of depth to width (a/h) of the scratch 13 generated by achip being about 0.1:

Kt=1+4×0.1=1.4   (2)

This follows that the stress at the bottom 14 of the scratch 13generated by a chip is about 1.4 times as large as the stress generatedwith no scratch present.

Next, with reference to FIGS. 5A and 5B, a case according to the presentembodiment of the present invention will be described. The sectionalshape in the direction of stress of a scratch 15 generated by a chip canbe approximated to a semi-ellipse with depth a and width h/cos θ. Thestress concentration factor Kt in the present embodiment is representedby expression (3) obtained by replacing h in expression 1 with h/cos θ.

$\begin{matrix}{{Kt} = {1 + {\frac{4\; a}{h}\cos \; \theta}}} & (3)\end{matrix}$

With the ratio of depth to width (a/h) of the scratch 15 generated by achip also being about 0.1 and the inclination θ of the scratch 15 being60°:

Kt=1+4×0.1×0.5=1.2   (4)

As described above, in the present embodiment in which the reamer usedto ream a pin insertion hole is removed while being rotated causing ascratch generated by a chip to be inclined by 60° as θ with respect tothe axial direction of the pin insertion hole, the stress concentrationfactor Kt is reduced to 1.2 compared with 1.4 obtained in a related-artcase in which the reamer is removed without being rotated causing ascratch generated by a chip to run along the axial direction of the pininsertion hole. Namely, the stress at the bottom of a scratch can bereduced by 14% (1−1.2/1.4≈0.14).

FIG. 6 is a graph showing an example relationship between stress rangeand fatigue life of a turbine blade made of a high-strength material.When, in the related-art case, the range of stress (range of stressvariation occurring between the start and end of the turbine operation)generated at the bottom 14 of the scratch 13 is 1500 MPa and the fatiguelife of the turbine blade is 5000 times, reducing the stress by 14%according to the present embodiment generates an effect of approximatelytripling the fatigue life to 15700 times.

Generally, a fatigue crack grows perpendicularly to the direction ofstress. Therefore, in the related-art case, if a crack is generated inthe scratch 13, it will grow along the bottom 14 of the scratchsubjected to a high stress. In the present embodiment, if a crack isgenerated in the scratch 15, it will grow following a path whichdeviates from the scratch 15 generated by a chip, so that the stress atthe front end of the growing crack is smaller than in the related-artcase. This is an effect lengthening the fatigue life of the turbineblade.

FIG. 7 is a graph showing a relationship between stress concentrationfactor Kt and scratch inclination θ based on expression (3) with 0.1assigned to a/h. As shown, when the inclination of the scratch 15generated by a chip is small, the stress concentration factor Kt is notadequately reduced. However, when a scratch on the inner surface of apin insertion hole in the turbine blade attachment base is inclined withrespect to the axial direction of the pin insertion hole, the directionof the scratch and the direction of tensile stress generated on theinner surface of the pin insertion hole are closer to be parallel toeach other than in the related-art case. This generates an effect ofreducing the fatigue strength reduction caused by the scratch. Note thatthe above described inclination of a scratch on the inner surface of apin insertion hole in the turbine blade attachment base with respect tothe axial direction of the pin insertion hole does not refer to aninclination resulting from a manufacturing error. The above describedinclination refers to an inclination of at least 10° or so.

According to the present embodiment, the inclination angle θ of thescratch is 60°, so that the direction of the scratch on the innersurface of the pin insertion hole and the direction of tensile stressgenerated on the inner surface of the pin insertion hole are adequatelyclose to be parallel to each other. This makes it possible toeffectively inhibit the fatigue strength reduction caused by thescratch. As seen from FIG. 7, when θ≧60°, the stress can be reduced by14% or more.

More generally, a target value of Kt dependent on the situation isdetermined and the minimum value of θ to be achieved to realize thetarget value of Kt is determined as expressed by expression (5) based onexpression (3).

$\begin{matrix}{\theta \geq {\cos^{- 1}\left\{ \frac{\left( {{Kt} - 1} \right)h}{4\; a} \right\}}} & (5)\end{matrix}$

As described above, an appropriate value of inclination θ of the scratch15 required to realize a target value of Kt can be obtained usingexpression (5).

Expression (5) can be satisfied by appropriately setting conditions forremoving the reamer 21. Where the radius of the reamer 21 is r (mm), therotation speed of the reamer 21 being removed is f (rpm), and the reamerremoval speed is v (mm/min), expression (6) is established representingthe relationships between the scratch inclination angle θ, the amount ofreamer movement per minute in the rotational direction, and the amountof reamer movement per minute in the removal direction as shown in FIG.8.

$\begin{matrix}{\theta = {\tan^{- 1}\left( {2\pi \; {r \cdot \frac{f}{v}}} \right)}} & (6)\end{matrix}$

Based on expressions (3), (5), and (6), the conditions for removing thereamer 21 without allowing stress concentration factor Kt to exceed atarget value are represented by expression (7).

$\begin{matrix}{{{Kt} \geq {1 + {\frac{4\; a}{h}\cos \; \theta}}} = {1 + {\frac{4\; a}{h}\sqrt{\frac{1}{1 + \left( {2\pi \; {r \cdot \frac{f}{v}}} \right)^{2}}}}}} & (7)\end{matrix}$

Where a/h=0.1 and Kt=1.2, expression (7) becomes as follows.

$\begin{matrix}{1.2 \geq {1 + {0.4\sqrt{\frac{1}{1 + \left( {2\pi \; {r \cdot \frac{f}{v}}} \right)^{2}}}}}} & (8)\end{matrix}$

When the radius r of the reamer 21 is 6 mm, the rotational speed f atwhich the reamer is removed and the removal speed v of the reamer arerequired to satisfy the following expression.

$\begin{matrix}{\frac{f}{v} \geq 0.046} & (9)\end{matrix}$

Thus, removing the reamer 21 based on the conditions satisfyingexpressions (7), (8), and (9) makes it possible to keep the stressconcentration factor Kt on a crack below a target value. Therefore,according to the present embodiment, high strength reliability can beobtained even in cases where a pin and finger root form is used forturbine blades made of a high-strength material with high notchsensitivity.

There are cases in which, when a hole is drilled, a burr removing drillis used in addition to a drill used to form the hole. The burr removingdrill is withdrawn from the drilled hole while being rotated so as toremove burrs. Unlike in drilling, however, burr generation is notconspicuous in reaming due to the nature of the process. Generally,therefore, reamers used for reaming are removed without being rotated.

Next, inspection of a crack generated on the inner surface of a pininsertion hole will be described. FIG. 9A schematically shows amicroscope 40 used to inspect the inner surface of a pin insertion hole8 after the hole is reamed and FIG. 9B shows a schematic sectional viewof portion A shown in FIG. 9A.

In the present embodiment, after a pin insertion hole is reamed, thereamer used for reaming is removed and the inner surface of the pininsertion hole is observed to make sure that the angle θ formed betweenthe scratch generated on the inner surface of the pin insertion hole andthe axial direction of the pin insertion hole is not smaller than apredetermined angle.

The microscope 40 is comprised of a rod-like scope body 41 and an imageprocessing/display device 45. The scope body 41 is provided, at a frontend portion thereof, with two cameras 42. For each of the cameras 42, alight 43 to be used as a light source for shooting the inner surface ofa pin insertion hole is provided close to the camera 42. The scope body41 is further provided with two rubber tires 44, one forwardly of thecameras 42 and the other rearwardly of the cameras 42. To inspect a pininsertion hole 8, the scope body 41 is inserted into the pin insertionhole 8, the inner surface of the pin insertion hole 8 is shot by thecameras 42, and the inner surface of the pin insertion hole 8 thus shotis displayed on the image processing/display device 45.

Referring to FIG. 9B, the cameras 42 can shoot, on both sides across theaxis of the pin insertion hole 8, such areas of the inner surface of thepin insertion hole 8 which range in angle, measured based on the axis ofthe pin insertion hole 8, from 50° to 130° with respect to 0°corresponding to the inner surface portion toward the rotor axis. The50° to 130° ranges on both sides across the axis of the pin insertionhole 8 cover areas of the inner surface of the pin insertion hole 8which are repeatedly subjected to a large tensile load while the turbineis rotating and which are desired to be free of circumferential surfaceirregularities. Therefore, moving the scope body 41 once through the pininsertion hole 8 can complete observation of the areas to be observed ofthe inner surface of the pin insertion hole 8.

The rubber tires 44 allow the cameras 42 to shoot the inner surface ofthe pin insertion hole 8 without coming into direct contact with theinner surface. The rubber tires 44 allow the scope body 41 to be movedinto and out of the pin insertion hole 8 smoothly without injuring theinner surface of the pin insertion hole 8.

As described above, the microscope 40 makes it possible, just byinserting the scope body 41 into the pin insertion hole, to quicklyobserve the inner surface of the pin insertion hole 8 without injuringthe pin insertion hole 8. This embodiment makes it possible todetermine, after the reamer is removed from a pin insertion hole,whether or not any scratch which might detrimentally affect the fatiguestrength of the turbine blade is present on the inner surface of the pininsertion hole. Namely, when the angle θ formed between a scratch on theinner surface of a pin insertion hole and the axial direction of the pininsertion hole is smaller than a predetermined value (for example, whenθ is such that a target stress concentration factor Kt cannot berealized based on the foregoing expression (5)), it is determined thatthe scratch may detrimentally affect the fatigue strength of the turbineblade. Based on this criterion, whether such a scratch is present on theinner surface of the pin insertion hole is determined. If such a scratchis found on the inner surface of the pin insertion hole, the scratch isremoved, for example, by grinding.

REFERENCE SIGNS LIST

-   2 Turbine blade-   3 Turbine rotor-   4 Blade section-   5 Blade fork-   6 Rotor disc-   7 Rotor fork-   8 Pin insertion hole-   9 Coupling pin-   10 Turbine rotary shaft-   11 Chip-   12 Fine chip-   13 Scratch (e.g. scratch 13 generated by a chip)-   14 Bottom (e.g. bottom 14 of the scratch)-   15 Scratch (e.g. scratch 15 generated by a chip)-   16 Bottom (e.g. bottom 16 of the scratch)-   20 Reaming machine-   21 Reamer-   22 Chuck section-   23 Air blower-   27 Arm-   28 Mount-   40 Microscope-   41 Scope body-   42 Camera-   43 Light-   44 Rubber tire

1. A method for manufacturing a multi-finger pinned root for turbineblade attached to a turbine rotor, the multi-finger pinned root couplinga turbine blade and a rotor disc of the turbine rotor, wherein a pininsertion hole is formed through a turbine blade attachment base throughsteps of: drilling a through-hole; reaming the drilled through-holeusing a reamer; and removing the reamer from the reamed through-holewhile rotating the reamer after the reaming.
 2. The method formanufacturing a multi-finger pinned root for turbine blade attached to aturbine rotor according to claim 1, wherein the reamer is removed at areamer rotation speed f (rpm) and a reamer removal speed v (mm/min) bothdetermined to satisfy the following expression (1): $\begin{matrix}{{Kt} \geq {1 + {\frac{4\; a}{h}\sqrt{\frac{1}{1 + \left( {2\pi \; {r \cdot \frac{f}{v}}} \right)^{2}}}}}} & (1)\end{matrix}$ where a/h is an aspect ratio (a=depth, h=width) of ascratch formed when the reamer is removed, Kt is an allowable stressconcentration factor, and r is a radius (mm) of the reamer.
 3. Themethod for manufacturing a multi-finger pinned root for turbine bladeattached to a turbine rotor according to claim 2, wherein, with 0.1assigned to a/h and 1.2 assigned to Kt in the expression (1), the reameris removed at a reamer rotation speed f (rpm) and a reamer removal speedv (mm/min) both determined to satisfy the following expression (2):$\begin{matrix}{1.2 \geq {1 + {0.4\sqrt{\frac{1}{1 + \left( {2\pi \; {r \cdot \frac{f}{v}}} \right)^{2}}}}}} & (2)\end{matrix}$
 4. The method for manufacturing a multi-finger pinned rootfor turbine blade attached to a turbine rotor according to claim 1,wherein, after the reamer is removed from the pin insertion hole, aninner surface of the pin insertion hole is observed to determine that anangle θ formed between a scratch formed on the inner surface of the pininsertion hole and an axial direction of the pin insertion hole is notsmaller than a predetermined angle.
 5. The method for manufacturing amulti-finger pinned root for turbine blade attached to a turbine rotoraccording to claim 2, wherein, after the reamer is removed from the pininsertion hole, an inner surface of the pin insertion hole is observedto determine whether an angle θ formed between a scratch formed on theinner surface of the pin insertion hole and an axial direction of thepin insertion hole satisfies the following expression (3):$\begin{matrix}{\theta \geq {\cos^{- 1}\left\{ \frac{\left( {{Kt} - 1} \right)h}{4\; a} \right\}}} & (3)\end{matrix}$
 6. The method for manufacturing a multi-finger pinned rootfor turbine blade attached to a turbine rotor according claim 4, whereinthe inner surface of the pin insertion hole is observed using amicroscope.
 7. The method for manufacturing a multi-finger pinned rootfor turbine blade attached to a turbine rotor according claim 5, whereinthe inner surface of the pin insertion hole is observed using amicroscope.
 8. The method for manufacturing a multi-finger pinned rootfor turbine blade attached to a turbine rotor according claim 4,wherein, of the inner surface of the pin insertion hole, only apredetermined area repeatedly subjected to a large tensile load whilethe turbine is rotating is observed.
 9. The method for manufacturing amulti-finger pinned root for turbine blade attached to a turbine rotoraccording claim 5, wherein, of the inner surface of the pin insertionhole, only a predetermined area repeatedly subjected to a large tensileload while the turbine is rotating is observed.
 10. The method formanufacturing a multi-finger pinned root for turbine blade attached to aturbine rotor according to claim 8, wherein the area to be observedranges from 50° to 130° with respect to 0° corresponding to a bottomtoward the axis of the turbine rotor of the inner surface of the pininsertion hole.
 11. The method for manufacturing a multi-finger pinnedroot for turbine blade attached to a turbine rotor according to claim 9,wherein the area to be observed ranges from 50° to 130° with respect to0° corresponding to a bottom toward the axis of the turbine rotor of theinner surface of the pin insertion hole.
 12. A turbine blade to bepin-coupled to a rotor disc of a turbine rotor, wherein a scratch formedon an inner surface of a pin insertion hole formed through the turbineblade is inclined with respect to an axial direction of the pininsertion hole.
 13. The turbine blade according to claim 12, wherein anangle θ formed between the scratch and the axial direction of the pininsertion hole satisfies the following expression (4): $\begin{matrix}{\theta \geq {\cos^{- 1}\left\{ \frac{\left( {{Kt} - 1} \right)h}{4\; a} \right\}}} & (4)\end{matrix}$ where a/h is an aspect ratio (a=depth, h=width) of thescratch formed on the inner surface of the pin insertion hole and Kt isan allowable stress concentration factor.
 14. The turbine bladeaccording to claim 13, wherein, with the aspect ratio a/h of the scratchbeing 0.1 and the allowable stress concentration factor Kt being 1.2,the angle θ formed between the scratch and the axial direction of thepin insertion hole is 60° or greater.
 15. A turbine blade for use in alast stage of a low-pressure turbine, the turbine blade being made of ahigh-strength material and having a blade fork portion to be pin-coupledwith a rotor fork formed on a rotor disc of a turbine rotor, wherein ascratch formed on an inner surface of a pin insertion hole formedthrough the blade fork portion is inclined with respect to an axialdirection of the pin insertion hole.